For image tasks, since eq:optobjective is differentiable in \(\tilde{\mathbf {x}}_i\)  and \(\tilde{y}_i\)  and the model parameter \(\mathbf {w}\)  is known to the server, the server can optimize eq:optobjective using gradient-based search. Doing so yields recovered samples \((\tilde{\mathbf {x}}_i,\tilde{y}_i)\)  that closely resemble actual samples \((\mathbf {x}_i,y_i)\)  in the batch. In practice this approach is highly effective, and follow-up works proposed several optimizations to further improve its recovery accuracy [1]}, [2]}, [3]}.
